BLeGhidn
Answered

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What is the present value of Php 185,567.35 due in 5 years and 3 months if money is 7% compound quarterly?​

Sagot :

AGboiiidn

[tex]\large{\mathcal{QUESTION:}}[/tex]

What is the present value of Php 185,567.35 due in 5 years and 3 months if money is 7% compound quarterly?

[tex] \\ [/tex]

[tex]\large{\mathcal{SOLUTION:}}[/tex]

Using the formula for present value:

  • [tex]\rm{P = F - P(1+\frac{r}{n})^{nt}}[/tex]

[tex] \\ [/tex]

Given:

  • F = 185,567.35
  • T = 5yrs and 3 months or 5.25
  • R = 7% or 0.07
  • N = quarterly or 4 times a year

[tex] \\ [/tex]

Solving ,

  • [tex]\rm{P = F - P(1+\frac{r}{n})^{nt}}[/tex]

  • [tex]\rm{P = 185,567.35 - P(1+\frac{0.07}{4})^{4×5.25}}[/tex]

  • [tex]\rm{P = 185,567.35 - P(1+0.0175)^{21}}[/tex]

  • [tex]\rm{P = 185,567.35 - P(1.0175)^{21}}[/tex]
  • [tex]\rm{P = 185,567.35 - P(1.439536814)}[/tex]

  • [tex]\rm{P = 185,567.35 - 1.439536814P}[/tex]

  • [tex]\rm{P + 1.439536814P= 185,567.35 }[/tex]

  • [tex]\rm{2.439536814P= 185,567.35 }[/tex]
  • [tex]\rm{P= 185,567.35 ÷ 2.439536814 }[/tex]

  • [tex]\rm{P=76,066.63238}[/tex]

Therefore , the present value is Php 76,066.63

[tex] \\ [/tex]

[tex]\large{\mathcal{ANSWER:}}[/tex]

  • the present value is Php 76,066.63

[tex] \\ [/tex]